Question: Solve for $x$ and $y$ using elimination. ${4x+2y = 30}$ ${3x-2y = 12}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $7x = 42$ $\dfrac{7x}{{7}} = \dfrac{42}{{7}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {4x+2y = 30}\thinspace$ to find $y$ ${4}{(6)}{ + 2y = 30}$ $24+2y = 30$ $24{-24} + 2y = 30{-24}$ $2y = 6$ $\dfrac{2y}{{2}} = \dfrac{6}{{2}}$ ${y = 3}$ You can also plug ${x = 6}$ into $\thinspace {3x-2y = 12}\thinspace$ and get the same answer for $y$ : ${3}{(6)}{ - 2y = 12}$ ${y = 3}$